The couple are also getting serious about their relationship. "They've spent a lot of time together and really enjoy each other's company," says the source. "John is entirely focused on Katy."

As for recent tabloid reports that Mayer has been flirting with other women and that Perry discovered text messages on his phone, the source says, "That is absolutely not true. John would never do that to her, and Katy really trusts John."

For Perry, the holidays this year are dramatically different from 2011's. Last December, her then-husband Russell Brand filed for divorce. Their marriage officially ended this past July.